Re: Contradicrtion-free mathemattics (The new nonstandard analysis

E. E. Escultura

>The three axioms are all listed in my first post of Jan. 5. At any rate, here are the
>axioms of the new real number system R*, +, x.

>1) R* contains the basic integers 0, 1, . . ., 9.
>2) The addition table
>3) The multiplication table.

Those aren't axioms in the sense that anyone else uses the word.  As
far as anyone can tell by reading statement 1,  R* is exactly the set
{0,1,2,3,4,5,6,7,8,9}.

I want a formal axiomatization in the sense of mathematical logic.  I
want the signature of your theory and the axioms written as formal
sentences in predicate calculus using that signature.  Only then can
you claim that you have actually stated the axioms.

You ignored my question about what you consider a proof to be.  What
inference rules do you allow?  How can you draw a conclusion that isn't
an axiom already?

.

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